A Momentum-Conserving Scheme for Flow Simulation in 1D Channel with Obstacle and Contraction

Abstract

We consider the extension of the momentum conservative staggered-grid (MCS) scheme for flow simulation in channels with varying depth and width. The scheme is formulated using the conservative properties of the Saint-Venant equations. The proposed scheme was successful in handling various steady flows and achieved results that are in complete accordance with the analytical steady solutions. Different choices of boundary conditions have created steady solutions according to the mass and energy conservations. This assessment has served as a validation of the proposed numerical scheme. Further, in a channel with a contraction and a nonuniform bed, we simulate two cases of dam break. The simulation results show a good agreement with existing experimental data. Moreover, our scheme, that uses a quasi-1-dimensional approach, has shown some fair agreement with existing 2-dimensional numerical results. This evaluation demonstrates the merits of the MCS scheme for various flow simulations in channels of varying width and bathymetry, suitable for river flow modeling.